Question: Solve for $x$ and $y$ by deriving an expression for $y$ from the second equation, and substituting it back into the first equation. $\begin{align*}6x-6y &= 4 \\ -9x-8y &= -6\end{align*}$
Answer: Begin by moving the $x$ -term in the second equation to the right side of the equation. $-8y = 9x-6$ Divide both sides by $-8$ to isolate $y$ $y = {-\dfrac{9}{8}x + \dfrac{3}{4}}$ Substitute this expression for $y$ in the first equation. $6x-6({-\dfrac{9}{8}x + \dfrac{3}{4}}) = 4$ $6x + \dfrac{27}{4}x - \dfrac{9}{2} = 4$ Simplify by combining terms, then solve for $x$ $\dfrac{51}{4}x - \dfrac{9}{2} = 4$ $\dfrac{51}{4}x = \dfrac{17}{2}$ $x = \dfrac{2}{3}$ Substitute $\dfrac{2}{3}$ for $x$ back into the top equation. $6( \dfrac{2}{3})-6y = 4$ $4-6y = 4$ $-6y = 0$ $y = 0$ The solution is $\enspace x = \dfrac{2}{3}, \enspace y = 0$.